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On the role played by extreme summands when a sum of independent and identically distributed random vectors is asymptotically α-stable

Part of: Stochastic processes Limit theorems

Published online by Cambridge University Press:  14 July 2016

Yu. Davydov  and
A. V. Nagaev
Yu. Davydov*
Affiliation:
Université des Sciences et Technologies de Lille
A. V. Nagaev*
Affiliation:
Nicolaus Copernicus University, Toruń
*
∗ Postal address: Laboratoire de Statistique et Probabilités, Bât. M2, FRE-CNRS 2222, Université des Sciences et Technologies de Lille, 59655 Villeneuve d’Ascq Cedex, France. Email address: youri.daydov@univ-lille1.fr
∗∗ Postal address: Nicolaus Copernicus University, Faculty of Mathematics and Informatics, UMK, 12/18 Chopin str, 87-100, Toruń, Poland. Email address: nagaev@mat.uni.torun.pl
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Abstract

The focus of our attention is the limit distribution of the sum of independent and identically distributed random vectors from which all the extreme summands are removed. The problem is rather trivial if the summands are ordered by their norms. It is of much more interest when the vertices of the convex hull generated by the vectors are taken as the extremes.

Keywords

Binomial and Poisson point processesPoisson spectral measureextreme valuesstable lawsconvex hullpeeling

MSC classification

Primary: 60F05: Central limit and other weak theorems
Secondary: 60G55: Point processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 2 , June 2004 , pp. 437 - 454
Copyright
Copyright © Applied Probability Trust 2004 

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